Question

Let $A=\{9,10,11,12,13\}$ and let $f:A\to N$ be defined by $f\left(n\right)=$ the highest prime factor of $n$. Find the range of $f$

Answer 1

$A=\{9,10,11,12,13\}$
$f:A\to N$ is defined as
$f\left(n\right)=$ The highest prime factor of $n$
Prime factor of $9=3$
Prime factors of $10=2,5$
Prime factors of $11=11$
Prime factors of $12=2,3$
Prime factors of $13=13$

$\therefore f\left(9\right)=$ The highest prime factor of $9=3$
$f\left(10\right)=$ The highest prime factor of $10=5$
$f\left(11\right)=$ The highest prime factor of $11=11$
$f\left(12\right)=$ The highest prime factor of $12=3$
$f\left(13\right)=$ The highest prime factor of $13=13$
Thus range of $f$ is the set of all $f\left(n\right)$ where $n\in A$
is $=\{3,5,11,13\}$